Day 159 brief — US calls a Hormuz deal 'imminent' as Iran denies any US talks in its own media; Trump concedes no immediate reopening; oil falls a second day; Qatar joins mediation

Day 159 opened with more of Washington's principals attaching their names to a deal Tehran still says does not exist. Treasury Secretary Scott Bessent said an agreement could be reached 'today or tomorrow' to open the Strait of Hormuz to 'freedom of movement'; Secretary of State Rubio said progress had been made; and President Trump called a deal 'imminent' — even as he branded Iran's leadership 'unbelievably duplicitous' and, per CBS News, floated a 'decapitation' threat (CBS News, ABC News, Washington Post, CNN). Iran hardened the other way: state outlet Tasnim reported that Tehran denies any US talks and limits negotiations to Oman on Hormuz alone, and a source close to the negotiating team denied any agreement to reopen the strait (Tasnim, Al Jazeera). One thing did move toward Tehran: Trump conceded the arrangement 'would not mean the immediate reopening' of Hormuz, narrowing the definitional gap that is the whole dispute. Qatar said progress had been made toward US-Iran talks to end the war, joining Oman and the Gulf as mediators (Haaretz). The oil market extended its de-escalation vote a second day — Brent fell toward $79-82, reversing earlier gains as diplomacy eased supply fears (Forbes, Trading Economics, Fortune). But the US and Israel kept preparing possible strikes on Iranian energy sites, Israel held at highest alert, and the Houthi embargo of Saudi Arabia held at Bab el-Mandeb (Haaretz, The Hill). Per §3.5.3 the claim now carries three US principals and a mediator, and the named counterparty still denies the channel. Direction holds mixed; seven-day and spillover risk hold critical; the thirty-day ceasefire probability edges up two points to 13.